function [diff, kappa_0, kappa_1, A_0, A_1] = mean_wc_LL(x,I)
    

    kappa_1 = exp(x)/(exp(x) + 1);
    kappa_0 = log(1 + exp(x)) - x * kappa_1;

    A_1 = (1 - 1/I.psi)/(1 - (1 - I.nu + I.phi * I.nu) * kappa_1); 
    A_0 = (log(I.delta) + kappa_0 + (1 - I.phi) * (1 - kappa_1 + I.nu * kappa_1) * I.mu * A_1 + 0.5 * (1 - 1/I.psi + kappa_1 * A_1 * I.phi * I.nu)^2 * I.theta * (1 + I. phi * I.nu) * I.sigma^2)/(1 - kappa_1);

    
    diff = x - A_0 - A_1*I.phi*I.mu;

end